|Set Theory: set theory is the system of rules and axioms, which regulates the formation of sets. The elements are exclusively numbers. Sets contain individual objects, that is, numbers as elements. Furthermore, sets contain sub-sets, that is, again sets of elements. The set of all sub-sets of a set is called the power set. Each set contains the empty set as a subset, but not as an element. The size of sets is called the cardinality. Sets containing the same elements are identical. See also comprehension, comprehension axiom, selection axiom, infinity axiom, couple set axiom, extensionality principle._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Set theory: seperate quantities have one element in common: the empty set - mereology: here, it does not exist. - Partial order: here is the common part the lower barrier - product: greatest lower barrier: - the individual, that x and y have in common - (= average of the set theory, lens in Venndiagram). - stronger: binary sum: is the individual who overlaps iff it at least overlaps one of x or y (Venndiagram: both circles with lens) - E.g. Broom sum of handle and head - any two individuals always have a sum.
Set Theory/Modality/necessity/Simons: rigidity of the element relationship: a class can have in no possible world other elements, as it has in the actual world. - This is analog to the mereological essentialism for subsets.
Set Theory/mereology/elements/(s): elements are not interchangeable - parts are._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Parts Oxford New York 1987